Liquid crystal displays (LCDs) have been widely employed in various applications, keeping moving towards thinner thickness and lower power consumption. As liquid crystal does not emit light, backlight modules are required to provide illumination rays. Mini light-emitting diodes (Mini-LEDs) have been considered promising light sources for ultra-thin direct-lit backlight modules. In the backlight module, double freeform surface lenses are usually employed to redistribute rays emitted by the chip and further reduce the optical distance (OD), further reducing the backlight module thickness. The common design of the lens is based on a point light source with the rays regulated by the lens to form a spot on the target plane and multiple spots superimposed to form the surface light source on the target plane of the Mini-LED backlight module. Therefore, the illuminance distribution of a single lens on the target plane is very important for the illuminance uniformity of the backlight module. Usually, the illuminance distribution of the target plane is directly set to uniform distribution or Gaussian distribution. However, in previous methods and algorithms, the simultaneous deterioration effects related to the number of Mini-LED chips, the distance between two adjacent lenses, and the optical distance have been ignored at the same time. The illuminance uniformity of the backlight module adopting the traditional method decreases, which causes troubles to the practical application. Therefore, it is necessary to reasonably design the illuminance value of the target plane based on a given array configuration and array pitches for ensuring the uniform illuminance distribution of the backlight module on a certain OD.

This paper proposes a design method to achieve uniform illumination with a high distance-height ratio (DHR). The principle of the method can obtain the illuminance distribution of a single lens on the target plane. The design is carried out in a backlight module with a Mini-LED number of P×Q and an array of Δpitch,x×Δpitch,y (Δpitch,x is pitch in x direction, and Δpitch,y is pitch in y direction). Firstly, on the target plane, the 2×2 Mini-LED array of the backlight module on a certain OD is divided into M×N mixing areas. A matrix I is employed to represent the illuminance values in the mixing areas and the illuminance distribution of a single lens on the target plane is represented by a vector X. By recording the amount of ray incident in each mixing area and the amount of energy carried by the rays, the method constructs the mapping matrix W between matrix I and vector X with a target plane spot radius R. Then, an ideal target plane illuminance distribution calculated by the LSQLIN iterative optimization algorithm is obtained. With this distribution, the light source-target plane energy mapping method is finally adopted to design a double freeform surface lens, which could obtain the double freeform surface lens profile. To verify the effectiveness of the proposed method, this paper generates the lens based on the traditional uniform distribution and Gaussian distribution methods for comparison and calculates the illumination uniformity of the array with the designed lens.

The design is carried out in a backlight module with a Mini-LED number of 5×5, an array of 39 mm×30 mm, and an optical distance of 6 mm. Then, the illuminance distribution of the single lens with a spot radius R=40 mm is designed. The illuminance distribution of the target plane by this method and the Gaussian distribution are obtained (Fig. 9). The illuminance distribution of the target plane obtained by this method is composed of discrete illuminance values, which is a non-smooth curve. This paper respectively designs the lens with uniform distribution, Gaussian distribution, and distribution based on this proposed method. The shape of the lens obtained from the three distribution designs shows that the overall size of the lens obtained from this design is the smallest (Fig. 10). The model is built in LightTools for array simulation, and the simulation results show that the lens designed by this method has the lowest degradation under the extended light source (Fig. 11). In the array configuration, the target plane illumination uniformity reaches 87.45%, which is 6.24% and 3.34% improvement over the commonly employed uniform and Gaussian distributions respectively. In addition, the simulation uniformity of the lens array designed by this method is higher than that of the methods based on uniform distribution and Gaussian distribution when the spot radius R of different target planes is designed (Table 1).

In this paper, a design method for a double freeform surface lens in Mini-LED backlight module is proposed to achieve uniform illumination. Based on a given array configuration and array pitches, the mapping matrix between the illuminance value of the target plane and the illuminance distribution of the single lens is established. The ideal target plane illuminance distribution is calculated by the LSQLIN iterative optimization algorithm. Then, with a spot radius R, a double freeform surface lens is designed by the light source-target plane energy mapping method. The lens could regulate the rays emitted from the Mini-LED chips to achieve uniform illumination on the target plane. A direct-lit Mini-LED backlight with an array of 39mm×30mm and an optical distance of 6mm is simulated to verify the proposed method. With R=40mm, the simulation results show that the illumination uniformity of 5×5 array with the designed lens reaches 87.45%, which realizes uniform illumination on the target plane. Compared with commonly employed uniform and Gaussian distributions, the uniformity improves by 6.24% and 3.34% respectively. At the same time, the smaller designed lens size can help manufacturers to save the generation cost. Consequently, the proposed method is an efficient way to design a double freeform surface lens in Mini-LED backlight module without extensive subsequent optimization work, which may open up an avenue for producing an ultra-thin and high illuminance uniformity direct-lit Mini-LED backlight module.